R^n上广义Radon变换的奇异值分解

The Singular Value Decomposition for Generalized Radon Transforms in R^n

当广义Radon变换限制在带权的平方可积函数空间时,该文构造了一类广义Radon变换的奇异值分解,给出了它们的逆变换的一些结果。

The singular value decompositions for the generalized Radon transforms are constructed when they are restricted to function spaces which are square integrable on R+n with known weight function W-n, some results about inverse transforms of the generalized Radon transforms are given. Furthermore, the inversion formulae and characteristics of their ranges are also developed.